A unified approach to blending of constant and varying parametric surfaces with curvature continuity

In this paper, we develop a new approach to blending of constant and varying parametric surfaces with curvature continuity. We propose a new mathematical model consisting of a vector-valued sixth-order partial differential equation (PDE) and time-dependent blending boundary constraints, and develop an approximate analytical solution of the mathematical model. The good accuracy and high computational efficiency are demonstrated by comparing the new approximate analytical solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on the continuity at trimlines, and apply the new approximate analytical solution in blending of constant and varying parametric surfaces with curvature continuit

Blending using ODE swept surfaces with shape control and C1 continuity

Surface blending with tangential continuity is most widely applied in computer aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: 1). exact satisfaction of 1C continuous blending boundary constraints, 2). effective shape control of blending surfaces, 3). high computing efficiency due to explicit mathematical representation of blending surfaces, and 4). ability to blend multiple (more than two) primary surfaces

C2 Continuous Blending of Time-Dependent Parametric Surfaces.

Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency

Differential equation-based shape interpolation for surface blending and facial blendshapes.

Differential equation-based shape interpolation has been widely applied in geometric modelling and computer animation. It has the advantages of physics-based, good realism, easy obtaining of high- order continuity, strong ability in describing complicated shapes, and small data of geometric models. Among various applications of differential equation-based shape interpolation, surface blending and facial blendshapes are two active and important topics. Differential equation-based surface blending can be time-independent and time-dependent. Existing differential equation-based surface blending only tackles time-dependen

CAD interface and framework for curve optimisation applications

Computer Aided Design is currently expanding its boundaries to include more design features in its processes. Design is identified as an iterative process converging to solutions satisfying a set of constraints. Its close relation with optimisation indicate that there is strong potential for the integration of optimisation and CAD. The problem addressed in this thesis lies in interfacing the geometric representation of design with other non-geometric aspects. The example of free-form curve modelling is taken to investigate such relationships. Assumptions are made that Optimisation is powered by Evolutionary Computing algorithms like Genetic Algorithms (GA). The geometric definition of curves is commonly supported by NURBS, whose construction constraints are defined locally at the data points. Here the NURBS formulation is used with GA in an attempt to provide complementary handles on the curves shape other than the usual data point coordinates and control points weights. Differential properties are used for optimising NURBS, Hermite interpolation allows for the definition of higher order constraints (tangent, normal, bi-normal) at data points. The assignment of parameter values at the data points, known as parameterisation also provides control of the curve’s shape. Curve optimisation is also performed at the geometric modelling level. Old mathematical theorems established by Frénet and further developed by other mathematicians provide means of defining a curve’s shape with it’s intrinsic equations. Such representation is possible by using Function Representation (F-rep) algebra available in the ACIS software. Frep allows more generic and exact means of interfacing with the curve’s geometry and new functionality for curve inspection and optimisation are proposed in this thesis. The integration of optimisation findings and CAD are documented in the definition of a framework. The framework architecture proposed reconstructs a new CAD environment from separate elements bolted together in a generic Application Programming Interface (API) named “Oli interface”. Functionality created to interface optimisation and CAD makes a requirement list of the work that both sides should undertake to achieve design optimisation in the CAD environment.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Creating Through Mind and Emotions

The texts presented in Proportion Harmonies and Identities (PHI) Creating Through Mind and Emotions were compiled to establish a multidisciplinary platform for presenting, interacting, and disseminating research. This platform also aims to foster the awareness and discussion on Creating Through Mind and Emotions, focusing on different visions relevant to Architecture, Arts and Humanities, Design and Social Sciences, and its importance and benefits for the sense of identity, both individual and communal. The idea of Creating Through Mind and Emotions has been a powerful motor for development since the Western Early Modern Age. Its theoretical and practical foundations have become the working tools of scientists, philosophers, and artists, who seek strategies and policies to accelerate the development process in different contexts

A Textbook of Advanced Oral and Maxillofacial Surgery

The scope of OMF surgery has expanded; encompassing treatment of diseases, disorders, defects and injuries of the head, face, jaws and oral cavity. This internationally-recognized specialty is evolving with advancements in technology and instrumentation. Specialists of this discipline treat patients with impacted teeth, facial pain, misaligned jaws, facial trauma, oral cancer, cysts and tumors; they also perform facial cosmetic surgery and place dental implants. The contents of this volume essentially complements the volume 1; with chapters that cover both basic and advanced concepts on complex topics in oral and maxillofacial surgery

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

2009 Annual Progress Report: DOE Hydrogen Program

This report summarizes the hydrogen and fuel cell R&D activities and accomplishments of the DOE Hydrogen Program for FY2009. It covers the program areas of hydrogen production and delivery; fuel cells; manufacturing; technology validation; safety, codes and standards; education; and systems analysis